Finite Group Databasebeta

← #23774892

Subgroups — #23774892

Order 10112.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579185C211yesmaximal, characteristic, complemented
2C22×#11929613C211yesmaximal, characteristic, complemented
3#19099219C211yesmaximal, characteristic, complemented
4#19099197C211yesmaximal, characteristic, complemented
5#19098951C211yesmaximal, characteristic, complemented
6#19098810C211yesmaximal, characteristic, complemented
7#19098777C211yesmaximal, characteristic, complemented
8#19098762C211yesmaximal, characteristic, complemented
9#19098715C211yesmaximal, characteristic, complemented
10#19098709C211yesmaximal, characteristic, complemented
11#19098701C211yesmaximal, characteristic, complemented
12#19098696C211yesmaximal, characteristic, complemented
13#19098662C211yesmaximal, characteristic, complemented
14#19098634C211yesmaximal, characteristic, complemented
15#466×C79C211yesmaximal, characteristic, complemented
16C2×#11929623C2211yescharacteristic, complemented
17C22×Dic158C2211yescharacteristic, complemented
18C22×D316C2211yescharacteristic
19C2×D4×D79—21no—
20C2×D4×D79C2211yescharacteristic
21#14579185—24no—
22C2×#11929613—24no—
23C2×#11929613C2211yescharacteristic
24C2×#11929613C2211yescharacteristic
25C2×#11929613C2211yescharacteristic, complemented
26C2×#11929613C2211yescharacteristic, complemented
27C2×#11929612C2211yescharacteristic, complemented
28C2×#11929612C2211yescharacteristic, complemented
29C2×#11929609C2211yescharacteristic
30C2×#11929609C2211yescharacteristic, complemented
31C2×#11929607C2211yescharacteristic, complemented
32#14579157C2211yescharacteristic
33#14579148C2211yescharacteristic, complemented
34#14579147—21no—
35#14579141C2211yescharacteristic, complemented
36#14579138—21no—
37#14579136C2211yescharacteristic
38#14579134—21no—
39#14579133—21no—
40#14579131—21no—
41#14579129—21no—
42#14579126C2211yescharacteristic, complemented
43D4×Dic79—21no—
44#14579123C2211yescharacteristic
45C4×C22⋊D79C2211yescharacteristic
46Dic79⋊C8C2211yescharacteristic, complemented
47#14579084C2211yescharacteristic, complemented
48#14579084C2211yescharacteristic, complemented
49#14579081C2211yescharacteristic
50#14579081C2211yescharacteristic, complemented
51C22⋊(C79⋊C8)C2211yescharacteristic, complemented
52(C2×D79)⋊C8C2211yescharacteristic, complemented
53#14579071C2211yescharacteristic, complemented
54C2×D8×C79C2211yescharacteristic, complemented
55C22×C8×C79C2211yescharacteristic, complemented
56#121×C79C2211yescharacteristic
57#121×C79C2211yescharacteristic, complemented
58#107×C79C2211yescharacteristic, complemented
59#102×C79C2211yescharacteristic, complemented
60#102×C79C2211yescharacteristic, complemented
61C23×D79—21no—
62C23×D79—21no—
63#11929623—22no—
64#11929623—41no—
65C2×Dic158—22no—
66C2×Dic158—21no—
67C2×Dic158—41no—
68C2×Dic158C2311yescharacteristic
69C2×Dic158C2311yescharacteristic
70C2×D316—21no—
71C2×D316—22no—
72C2×D316—21no—
73C2×D316—41no—
74C2×D316C2311yescharacteristic
75C2×D316C2311yescharacteristic
76C2×C22⋊D79—21no—
77C2×C22⋊D79—21no—
78C2×C22⋊D79—21no—
79C2×C22⋊D79—21no—
80C2×C22⋊D79D411yescharacteristic
81D4×D79—22no—
82D4×D79—44no—
83D4×D79—41no—
84C22×Dic79—21no—
85C22×Dic79—21no—
86C2×C4×D79—21no—
87C2×C4×D79C2311yescharacteristic
88#11929613—22no—
89#11929613—22no—
90#11929613—22no—
91#11929613D414yescomplemented
92#11929612—22no—
93#11929612—41no—
94#11929609—22no—
95#11929609—41no—
96#11929607—22no—
97C2×C79⋊C8C2311yescharacteristic
98C2×C79⋊C8C2311yescharacteristic
99C4⋊Dic79—21no—
100Dic79⋊C4—21no—
101Dic79⋊C4D411yescharacteristic
102C22⋊Dic79—21no—
103C22⋊Dic79—21no—
104C22⋊Dic79D411yescharacteristic
105(C2×D79)⋊C4—21no—
106(C2×D79)⋊C4—21no—
107(C2×D79)⋊C4—21no—
108(C2×D79)⋊C4D411yescharacteristic
109C4×Dic79—21no—
110C4×Dic79C2311yescharacteristic
111C2×D4×C79—21no—
112C2×D4×C79—21no—
113C2×D4×C79C2311yescharacteristic
114C2×D4×C79C2311yescharacteristic
115C22×C4×C79C2311yescharacteristic
116D8×C79—22no—
117C2×C8×C79—22no—
118C2×C8×C79C2311yescharacteristic
119C2×C8×C79C2311yescharacteristic
120C4⋊C4×C79C2311yescharacteristic
121C4⋊C4×C79C2311yescharacteristic
122C22⋊C4×C79—21no—
123C22⋊C4×C79—21no—
124C23×C79—21no—
125C23×C79—21no—
126C23×C79C2×D411yescharacteristic
127C22×D79—21no—
128C22×D79—21no—
129C22×D79—42no—
130C22×D79—42no—
131C22×D79—42no—
132C22×D79—42no—
133C22×D79—81no—
134C22×D79—81no—
135C22×D79C2×D411yescharacteristic
136D4×C79—21no—
137D4×C79—21no—
138D4×C79—21no—
139D4×C79—21no—
140D4×C79—42no—
141D4×C79—42no—
142C2×C4×C79—21no—
143C2×C4×C79—21no—
144C2×C4×C79—21no—
145C2×C4×C79—21no—
146C2×C4×C79C2×D411yescharacteristic
147C2×C4×C79C2411yescharacteristic
148C22⋊D79—22no—
149C22⋊D79—42no—
150C22⋊D79—42no—
151C22⋊D79—42no—
152C22⋊D79—81no—
153C2×Dic79—21no—
154C2×Dic79—21no—
155C2×Dic79—42no—
156C2×Dic79—42no—
157C2×Dic79C2×D411yescharacteristic
158C2×Dic79C2×D411yescharacteristic
159C2×Dic79C2×D411yescharacteristic
160D316—21no—
161D316—21no—
162D316—21no—
163D316—42no—
164D316—42no—
165D316C2×D412yes—
166C4×D79—21no—
167C4×D79—21no—
168C4×D79—42no—
169Dic158—21no—
170Dic158—21no—
171Dic158—21no—
172Dic158—42no—
173Dic158C2×D412yescomplemented
174C8×C79—21no—
175C8×C79C2×D412yescomplemented
176C79⋊C8—21no—
177C79⋊C8—21no—
178C22×C79—21no—
179C22×C79—21no—
180C22×C79—41no—
181C22×C79—41no—
182C22×C79—41no—
183C22×C79—41no—
184C22×C79—41no—
185C22×C79—41no—
186C22×C79AGL(1,ℤ/8)12yescomplemented
187C22×C79C22×D411yescharacteristic
188C2×D79—21no—
189C2×D79—22no—
190C2×D79—21no—
191C2×D79—21no—
192C2×D79—41no—
193C2×D79—41no—
194C2×D79—41no—
195C2×D79—41no—
196C2×D79—41no—
197C2×D79—84no—
198C2×D79—84no—
199C4×C79—21no—
200C4×C79—41no—
201C4×C79—41no—
202C4×C79C22×D411yescharacteristic
203C4×C79H(5,𝔽2)11yescharacteristic
204Dic79—21no—
205Dic79—22no—
206Dic79—21no—
207Dic79—21no—
208Dic79—41no—
209C2×C79—22no—
210C2×C79—81no—
211C2×C79—81no—
212C2×C79D4211yescharacteristic
213C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
214C2×C79#57711yescharacteristic
215D79—41no—
216D79—42no—
217D79—81no—
218#3265—791nomaximal, Sylow
219C79#326511yescharacteristic, complemented, Sylow
220C2×AGL(1,ℤ/8)—791no—
221C22×SD16—791no—
222#548—791no—
223D42—791no—
224#496—791no—
225#468—791no—
226#466D7911yescharacteristic, complemented
227#463—791no—
228#460—791no—
229#450—791no—
230#449—791no—
231#448—791no—
232#447—791no—
233#440—791no—
234#435—791no—
235C2×#41—791no—
236C22×Q8—791no—
237C22×D4—791no—
238C22×D4—791no—
239C22×D4—1581no—
240AGL(1,ℤ/8)—1584no—
241C2×SD16—791no—
242C2×SD16—791no—
243C2×SD16—791no—
244C2×SD16—791no—
245C2×SD16—791no—
246C2×SD16—791no—
247C2×SD16—1584no—
248C2×D8—791no—
249C2×D8—791no—
250C2×D8C2×D7911yescharacteristic, complemented
251C2×M16—791no—
252C22×C8C2×D7911yescharacteristic, complemented
253#127—791no—
254#124—791no—
255#124—1581no—
256C22⋊Q8—791no—
257C22⋊Q8—1581no—
258#121—791no—
259#121—1581no—
260#121—1581no—
261#121C2×D7911yescharacteristic
262#121C2×D7911yescharacteristic, complemented
263#120—1581no—
264#120—1581no—
265C4×Q8—791no—
266C4×D4—791no—
267C4×D4—791no—
268C4×D4—1581no—
269#107C2×D7911yescharacteristic, complemented
270C4⋊C8—791no—
271#103—791no—
272#103—791no—
273#102—791no—
274#102—791no—
275#102C2×D7911yescharacteristic, complemented
276#102C2×D7911yescharacteristic, complemented
277C22⋊C8—791no—
278C22⋊C8—791no—
279#97—791no—
280C24—1581no—
281C24—1581no—
282#41—3161no—
283#41—1582no—
284C2×Q8—3161no—
285C2×Q8—791no—
286C2×Q8—791no—
287C2×Q8—1582no—
288C2×Q8—1581no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—3161no—
292C2×D4—3164no—
293C2×D4—3161no—
294C2×D4—791no—
295C2×D4—791no—
296C2×D4—791no—
297C2×D4—1581no—
298C2×D4—1582no—
299C2×D4—1581no—
300C2×D4—1581no—
301C2×D4—1581no—
302C2×D4—1582no—
303C2×D4—1581no—
304C2×D4—1581no—
305C2×D4C22×D7911yescharacteristic
306C2×D4C22×D7911yescharacteristic
307C22×C4—791no—
308C22×C4—1581no—
309C22×C4—1581no—
310C22×C4—1581no—
311C22×C4C22×D7911yescharacteristic
312SD16—3161no—
313SD16—794no—
314SD16—1582no—
315SD16—1582no—
316SD16—1582no—
317SD16—1582no—
318D8—22no—
319D8—3161no—
320D8—1582no—
321M16—1582no—
322C2×C8—22no—
323C2×C8—791no—
324C2×C8—791no—
325C2×C8C22×D7911yescharacteristic
326C2×C8C22×D7911yescharacteristic
327C4⋊C4—791no—
328C4⋊C4—1581no—
329C4⋊C4—1581no—
330C4⋊C4C22×D7911yescharacteristic
331C4⋊C4C22×D7911yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—791no—
335C22⋊C4—791no—
336C22⋊C4—1581no—
337C22⋊C4—1581no—
338C22⋊C4—1581no—
339C22⋊C4—1581no—
340C22⋊C4—1581no—
341C42—791no—
342C42—1581no—
343C23—21no—
344C23—21no—
345C23—3162no—
346C23—3162no—
347C23—3162no—
348C23—3162no—
349C23—791no—
350C23—6321no—
351C23—6321no—
352C23—1581no—
353C23—1581no—
354C23D4×D7911yescharacteristic
355Q8—3162no—
356Q8—792no—
357Q8—1581no—
358Q8—1581no—
359Q8—1581no—
360D4—21no—
361D4—21no—
362D4—21no—
363D4—21no—
364D4—42no—
365D4—42no—
366D4—3162no—
367D4—3162no—
368D4—3162no—
369D4—3162no—
370D4—3162no—
371D4—792no—
372D4—6321no—
373D4—1582no—
374D4—1581no—
375D4—1581no—
376D4—1581no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—3162no—
382C2×C4—3162no—
383C2×C4—3162no—
384C2×C4—791no—
385C2×C4—791no—
386C2×C4—791no—
387C2×C4—1581no—
388C2×C4—1581no—
389C2×C4—1581no—
390C2×C4—1581no—
391C2×C4D4×D7911yescharacteristic
392C2×C4C23×D7911yescharacteristic
393C8—21no—
394C8—1581no—
395C8—1581no—
396C8D4×D7912yescomplemented
397C22—21no—
398C22—21no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—3161no—
406C22—3161no—
407C22—3161no—
408C22—3161no—
409C22—3161no—
410C22—6324no—
411C22—6324no—
412C22—1581no—
413C22—1582no—
414C22—1581no—
415C22—1581no—
416C22#1457918512yescomplemented
417C22C2×D4×D7911yescharacteristic
418C4—21no—
419C4—41no—
420C4—41no—
421C4—3161no—
422C4—1581no—
423C4—1582no—
424C4—1581no—
425C4—1581no—
426C4C2×D4×D7911yescharacteristic
427C4#1457920711yescharacteristic
428C2—22no—
429C2—81no—
430C2—81no—
431C2—3162no—
432C2—3161no—
433C2—6321no—
434C2#1909919711yescharacteristic
435C2C2×#1457918511yescharacteristic
436C2#1909937011yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#466×C79C2
socleC22×C79C22×D4
hypercenter#466D79
hypocenterC79#3265
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#14579185C2semidirect
2. C22×#11929613C2semidirect
3. #19099219C2semidirect
4. #19099197C2semidirect
5. #19098951C2semidirect
6. #19098810C2semidirect
7. #19098777C2semidirect
8. #19098762C2semidirect
9. #19098715C2semidirect
10. #19098709C2semidirect
11. #19098701C2semidirect
12. #19098696C2semidirect
13. #19098662C2semidirect
14. #19098634C2semidirect
15. #466×C79C2semidirect
16. C2×#11929623C22semidirect
17. C22×Dic158C22semidirect
25. C2×#11929613C22semidirect
26. C2×#11929613C22semidirect
27. C2×#11929612C22semidirect
28. C2×#11929612C22semidirect
30. C2×#11929609C22semidirect
31. C2×#11929607C22semidirect
33. #14579148C22semidirect
35. #14579141C22semidirect
42. #14579126C22semidirect
46. Dic79⋊C8C22semidirect
47. #14579084C22semidirect
48. #14579084C22semidirect
50. #14579081C22semidirect
51. C22⋊(C79⋊C8)C22semidirect
52. (C2×D79)⋊C8C22semidirect
53. #14579071C22semidirect
54. C2×D8×C79C22semidirect
55. C22×C8×C79C22semidirect
57. #121×C79C22semidirect
58. #107×C79C22semidirect
59. #102×C79C22semidirect
60. #102×C79C22semidirect
91. #11929613D4semidirect
173. Dic158C2×D4semidirect
175. C8×C79C2×D4semidirect
186. C22×C79AGL(1,ℤ/8)semidirect
219. C79#3265semidirect
226. #466D79semidirect
250. C2×D8C2×D79semidirect
252. C22×C8C2×D79semidirect
262. #121C2×D79semidirect
269. #107C2×D79semidirect
275. #102C2×D79semidirect
276. #102C2×D79semidirect
396. C8D4×D79semidirect
416. C22#14579185semidirect